Digital pre-distortion device and method for a broadband power amplifier

ABSTRACT

According to the present invention, a digital pre-distortion device and method for use in a dynamic spectrum allocation system, which uses a breadband frequency range, such as a cognitive radio (CR) system, are implemented. Also, while as conventional pre-distortion device only enable the linearization of a signal of a fundamental frequency band, the digital pre-distortion device and method according to the present invention enable not only the linearization of a basic signal on frequency f c , but also simultaneously enable the elimination of harmonic signals on the high frequencies of 2f c , 3f c , 4f c , etc. The digital pre-distortion device for a broadband power amplifier according to a preferred embodiment of the present invention comprises: a nonlinear power amplifier; an equivalent amplifier model estimator; N pre-distorters; and a coefficient extractor for extracting the coefficients of the N pre-distorters.

TECHNICAL FIELD

The present invention relates, in general, to a digital predistortiondevice and method and, more particularly, to a digital predistortiondevice and method for a broadband power amplifier, which are operated ina dynamic spectrum allocation system that utilizes a broadband frequencyrange, as in the case of a Cognitive Radio (CR) system.

BACKGROUND ART

With an exponential increase in communication demands such as mobilecommunication, television (TV) broadcasting, a local area network, or ametropolitan area network, limited frequency resources have almostreached a saturation state. Therefore, technologies for efficientlydistributing and utilizing limited frequency resources have recentlyattracted attention.

Among these technologies, research into Cognitive Radio (CR) has beenactively conducted, which can recognize the current condition of use offrequency bands that are continuously changed, select an availablefrequency band, and utilize the available frequency band withoutinterfering with a conventional radio environment, thus maximizing thefrequency usage rate.

CR is a scheme for searching a spectrum of a very wide frequency range,utilizing a currently usable frequency band, controlling a carrierfrequency and bandwidth, and transmitting signals, rather than a schemefor transmitting signals using a fixed carrier frequency as in the caseof a conventional communication scheme. That is, a CR system ischaracterized in that, after a very wide band has been searched,transmission can be performed using any frequency band.

In the conventional communication system, the transmission bandwidth(BW) of signals is generally much smaller than a carrier frequency f_(c)(f_(c)>>BW). Therefore, harmonic signals occurring at integer multiplesof f_(c) (2f_(c), 3f_(c), 4f_(c), . . . ) due to the nonlinearcharacteristics of a power amplifier are undesirable signals, and can beeasily eliminated by a filter at the output terminal of the amplifier.

However, as described above, the CR system must take into considerationa wide band compared to the conventional communication system, and acarrier frequency and bandwidth must be freely changed in thecorresponding band, so that the transmission bandwidth to be consideredis much greater than the carrier frequency (f_(c)<<BW). Therefore, theoutput filter of the amplifier has a wideband pass function withoutcausing only a specific frequency to pass therethrough. Consequently, atransmittable frequency band ranges over a wide band, so that harmonicsignals generated by the amplifier may fall within the correspondingcommunication band, thus making it difficult to eliminate the harmonicsignals at the output terminal of the amplifier. That is, since thefrequency of harmonic signals may be used to transfer transmissionsignals as occasion demands, a specific frequency filter cannot beinstalled. Further, in the CR system, the carrier frequency of signalsdesired to be transmitted is dynamically changed, so that harmonicsignals are also dynamically changed, thus making it difficult toeliminate harmonic signals caused by nonlinear output signals by using afilter or the like.

When these harmonic signals are not eliminated, they influence theconventional communication system, such as by acting as interference tothe conventional communication system, in a system borrowing anyavailable spectrum, as in the case of the CR system, and thus theharmonic signals must be eliminated.

DISCLOSURE Technical Problem

Accordingly, the present invention has been made keeping in mind theabove problems occurring in the prior art, and an object of the presentinvention is to provide a digital predistortion device and method, whichare operated in a dynamic spectrum allocation system that utilizes awide band frequency range, as in the case of a CR system.

Another object of the present invention is to provide a digitalpredistortion device and method, which can simultaneously linearize afundamental signal at the location of a frequency f_(c) and eliminateharmonic signals generated at the locations of high frequencies of2f_(c), 3f_(c), 4f_(c), . . . , whereas a conventional predistortiondevice is intended to merely linearize a signal in a fundamentalfrequency band.

Technical Solution

A digital predistortion device according to a preferred embodiment ofthe present invention includes a nonlinear power amplifier foramplifying N input signals generated by a random signal generator, andthen generating N output signals; an equivalent amplifier modelestimator for receiving the N input signals and the N output signals,and estimating characteristics of the nonlinear power amplifier; acoefficient extractor for extracting coefficients of N predistortersusing the estimated characteristics of the nonlinear power amplifier;and N predistorters for eliminating or compensating for all or part ofthe N output signals.

Further, the N predistorters may include N-1 harmonic eliminationpredistorters for eliminating second to Nth harmonic signals from the Noutput signals of the nonlinear power amplifier; and a fundamentalsignal predistorter for compensating for nonlinear characteristics of afundamental signal among the N output signals of the nonlinear poweramplifier.

A digital predistortion device according to another preferred embodimentof the present invention may further include Digital to AnalogConverters (ADCs) for converting the N input signals into analogsignals; first mixers for upconverting the N signals converted intoanalog signals; real operators for selecting real number signals fromamong the upconverted signals; second mixers for downconverting the Noutput signals of the nonlinear power amplifier; Analog to DigitalConverters (ADCs) for converting the downconverted signals into digitalsignals; and low pass filters for eliminating image signals from thesignals converted into the digital signals.

Further, the coefficient extractor may be configured to first extract acoefficient of a harmonic elimination predistorter corresponding to aharmonic of a highest frequency among the N-1 harmonic eliminationpredistorters, and then extract coefficients of harmonic eliminationpredistorters corresponding to harmonics of lower frequencies by stages.

Furthermore, the coefficient extractor may be configured to extract andfix all coefficients of the harmonic elimination predistorters, andthereafter extract a coefficient of the fundamental signal predistorter.

In detail, a digital predistortion method according to a preferredembodiment of the present invention includes (a) a random signalgenerator generating N input signals; (b) a nonlinear power amplifieramplifying the generated N input signals, and then generating N outputsignals; (c) an equivalent amplifier model estimator receiving the Ninput signals and the N output signals, and estimating characteristicsof the nonlinear power amplifier; (d) a coefficient extractor extractingcoefficients for N-1 harmonic elimination predistorters and a singlefundamental signal predistorter using the estimated characteristics ofthe nonlinear power amplifier; (e) the N-1 harmonic eliminationpredistorters eliminating second or higher harmonic signals from the Noutput signals; and (f) the fundamental signal predistorter compensatingfor nonlinear characteristics occurring in a fundamental signal amongthe N output signals.

Further, the digital predistortion method may further include, between(a) and (b), (a-1) Digital to Analog Converters (DACs) converting the Ninput signals into analog signals; (a-2) first mixers upconverting thesignals converted into the analog signals; (a-3) real operatorsselecting real number signals from among the upconverted signals; and(a-4) inputting the real number signals selected at (a-3) to thenonlinear power amplifier.

Furthermore, the digital predistortion method may further include,between (b) and (c), (b-1) inputting the N output signals of thenonlinear power amplifier to second mixers and downconverting the Noutput signals; (b-2) Analog to Digital Converters (ADCs) converting thedownconverted signals into digital signals; and (b-3) low pass filterseliminating imagine signals from the signals converted into the digitalsignals.

In detail, (d) may include first extracting a coefficient of a harmonicelimination predistorter corresponding to a harmonic of a highestfrequency among the N-1 harmonic elimination predistorters, and thenextracting coefficients of harmonic elimination predistorterscorresponding to harmonics of lower frequencies by stages; andextracting and fixing all coefficients of the N-1 harmonic eliminationpredistorters, and thereafter extracting a coefficient of thefundamental signal predistorter.

Advantageous Effects

In accordance with a digital predistortion device and method of thepresent invention, there can be provided a digital predistortion deviceand method which are operated in a dynamic spectrum allocation systemthat utilizes a wide band frequency range, as in the case of a CRsystem.

Further, a conventional predistortion device has the effect of merelylinearizing only a signal in a fundamental frequency band, whereas thepresent invention can implement a digital predistortion device andmethod which simultaneously linearize a fundamental signal at thelocation of a frequency f and eliminate harmonic signals generated atthe locations of high frequencies of 2f_(c), 3f_(c), 4f_(c), . . . .

DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram showing a comparison between a conventionalcommunication system and a Cognitive Radio (CR) system;

FIG. 2 illustrates a diagram showing the pass band transmitter model ofthe conventional communication system;

FIG. 3 illustrates an embodiment of a predistortion device foreliminating harmonic signals generated due to the nonlinearcharacteristics of a nonlinear power amplifier;

FIG. 4 illustrates intermodulation terms when K=3;

FIG. 5 is a configuration diagram showing a predistortion deviceaccording to a preferred embodiment of the present invention;

FIG. 6 is a flowchart showing a digital predistortion method accordingto a preferred embodiment of the resent invention;

FIG. 7 is a diagram showing the procedure of preprocessing input signalsto be input to a nonlinear power amplifier;

FIG. 8 is a flowchart showing signals to be input to an equivalentamplifier model estimator;

FIG. 9 is a flowchart showing the extraction of coefficients by acoefficient extractor;

FIG. 10 illustrates a simulation environment for verifying the effect ofthe present invention;

FIG. 11 illustrates the performance of harmonic elimination according toan embodiment of the present invention;

FIG. 12 illustrates the frequency spectrum of a fundamental signalaccording to an embodiment of the present invention;

FIG. 13 is a diagram showing the frequency spectrum of a second harmonicsignal according to an embodiment of the present invention; and

FIG. 14 is a diagram showing the frequency spectrum of a third harmonicsignal according to an embodiment of the present invention.

Description of reference characters of principal parts  10: nonlinearpower amplifier  20: equivalent amplifier model estimator  30:coefficient extractor  40: predistorter 50: DAC  60: first mixer 70:real operator  80: second mixer 90: ADC 100: low pass filter

BEST MODE

Hereinafter, a digital predistortion device and method for a broadbandpower amplifier according to embodiments of the present invention willbe described in detail with reference to the attached drawings.

It is apparent that the following embodiments of the present inventionare merely intended to embody the present invention and are not intendedto restrict or limit the scope of the present invention. Contents thatcan be easily inferred by those skilled in the art from the detaileddescription and embodiments of the present invention are interpreted asbeing included in the scope of the present invention.

First, a comparison between a conventional communication system and aCognitive Radio (CR) system is shown in FIG. 1.

As can be seen from FIG. 1(A), the transmission bandwidth (BW) ofsignals in the conventional communication system is generally muchsmaller than a carrier frequency f_(c) (f_(c)>>BW). Therefore, harmonicsignals generated at integer multiples of f_(c) (2f_(c), 3f_(c), 4f_(c),. . . , ) due to the nonlinear characteristics of the power amplifierare undesirable signals and can be easily eliminated by a filter at theoutput terminal of the amplifier.

However, as can be seen from FIG. 1(B), in a dynamic spectrum allocationsystem that utilizes a wide band frequency range, as in the case of theCR system, a band that is wider than that of the conventionalcommunication system must be taken into consideration, and a carrierfrequency and bandwidth must be able to be freely changed within thecorresponding band, so that the transmission bandwidth to be consideredis much greater than the carrier frequency (f_(c)<<BW). Therefore, theoutput filter of the amplifier has a wide band-pass function withoutcausing only a specific frequency to pass therethrough. Consequently, atransmittable frequency band ranges over a wide band, so that harmonicsignals generated in the amplifier may fall within the correspondingcommunication band, thus making it difficult to eliminate the harmonicsignals at the output terminal of the amplifier.

Therefore, an object of a conventional predistortion transmitter is tolinearize only a signal in a fundamental frequency band, whereas thepresent invention needs to simultaneously linearize a fundamental signalat the location of a frequency f_(c) and eliminate harmonic signalsgenerated at the locations of high frequencies of 2f_(c), 3f_(c),4f_(c), . . . .

Below, differences between the predistortion devices and methods of theconventional communication system and the dynamic spectrum allocationsystem, such as the CR system, will be described in detail.

Conventional Communication System

In FIG. 2, the pass band transmitter model of the conventionalcommunication system is shown.

A complex signal y(n) is converted into an analog signal y(t) by aDigital to Analog Converter (DAC), and y(t) is upconverted by a mixerand is then converted into a real number signal z(t). After z(t) hasbeen amplified by a nonlinear power amplifier, it is transmitted,wherein a nonlinear power amplifier G_(p)( ) is represented by aKth-degree polynomial, as given in the following Equation 1:

$\begin{matrix}{{a(t)} = {\sum\limits_{k}^{K}\; {\alpha_{k}{z^{k}(t)}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where {α_(k)} denotes a coefficient indicating the characteristics ofthe nonlinear power amplifier. In order to consider the influence of thenonlinear characteristics of the nonlinear power amplifier, a relationalexpression of a passband and a baseband, given in the following Equation2, is used:

z(t)=Re {y(t)e ^(jω) ⁰ ^(t)}=½[y(t)e ^(jω) ⁰ ^(t) +y ^(t)(t)e ^(˜jω) ⁰^(t)]  Equation 2

where ω₀=2πf_(c), and f_(c) denotes a carrier frequency. When Equation 2is applied to Equation 1, an equation such as Equation 3 can beobtained:

$\begin{matrix}{{{a(t)} = {{a_{0}(t)} + \left\lbrack {{^{{j\omega}_{o}t}{a_{1}(t)}} + {^{{- {j\omega}_{o}}t}{a_{1}^{*}(t)}}} \right\rbrack + \left\lbrack {{^{{j2\omega}_{o}t}{a_{2}(t)}} + {^{{- {j2\omega}_{o}}t}{a_{2}^{*}(t)}}} \right\rbrack + \left\lbrack {{^{{j3\omega}_{o}t}{a_{3}(t)}} + {^{{- {j3\omega}_{o}}t}{a_{3}^{*}(t)}}} \right\rbrack + \ldots}}\mspace{79mu} {where}\mspace{79mu} {{{a_{0}(t)} = {\sum\limits_{k}^{\;}{\alpha_{k}\frac{\begin{pmatrix}{2k} \\k\end{pmatrix}}{2^{2k}}{{y(t)}}^{2k}}}},\mspace{79mu} {{a_{1}(t)} = {\sum\limits_{k}^{\;}{\alpha_{k}\frac{\begin{pmatrix}{{2k} + 1} \\k\end{pmatrix}}{2^{{2k} + 1}}{{y(t)}}^{2k}{y(t)}}}},\mspace{79mu} {{a_{2}(t)} = {\sum\limits_{k}^{\;}{\alpha_{k}\frac{\begin{pmatrix}{2k} \\{k + 1}\end{pmatrix}}{2^{2k}}{{y(t)}}^{2k}{y(t)}^{2}}}},\mspace{79mu} {{a_{3}(t)} = {\sum\limits_{k}^{\;}{\alpha_{k}\frac{\begin{pmatrix}{{2k} + 1} \\{k + 1}\end{pmatrix}}{2^{{2k} + 1}}{{y(t)}}^{2k}{y(t)}^{3}}}},\ldots \mspace{14mu},}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

and a₀(t) denotes an output signal at a Direct Current (DC) location,a₁(t) denotes a fundamental signal that is the first harmonic signal ofa transmission signal, a₂(t) denotes the second harmonic signal of thetransmission signal, and a₃(t) denotes the third harmonic signal of thetransmission signal. The conventional predistortion technique consideredonly the linearization of the fundamental signal a₁(t), and did notconsider second or higher harmonic signals generated due to nonlinearcharacteristics. However, in the dynamic spectrum allocation system,such as the CR system, second or higher harmonic signals must beeliminated. Therefore, the present invention presents a predistortionalgorithm which considers both the elimination of second or higherharmonic signals and the linearization of the fundamental signal.

Dynamic Spectrum Allocation System

FIG. 3 illustrates an embodiment of a typical predistortion devicecapable of eliminating harmonic components generated at the output of anonlinear power amplifier.

Predistorters are located at respective locations corresponding tointeger multiples of a carrier frequency in a baseband, F₁( ) denotes afundamental signal predistorter for linearizing a fundamental signal,and F₂( ), F₃( ), . . . respectively denote harmonic eliminationpredistorters for eliminating second, third, and higher harmonicsignals.

The output signal of a multi-input transmitter, as shown in FIG. 3 has avery complicated form due to the nonlinear characteristics of theamplifier. A description will be made based on an embodiment when N=3.When it is assumed that y₁(t), y₂(t), and y₃(t) are respective inputs ofthe nonlinear power amplifier, if z₁(t)=Re {y₁(t)e^(jω) ⁰ ^(t)},z₂(t)=Re {y₂(t)e^(j2ω) ⁰ ^(t)}, z₃(t)=Re {y₃(t)e^(j3ω) ⁰ ^(t)}, andz(t)=z₁(t)+z₂(t)+z₃(t) are applied to Equation 1, the following Equation4 can be obtained:

$\begin{matrix}{{{{a(t)} = {{a_{0}(t)} + \left\lbrack {{^{{j\omega}_{0}t}{a_{1}(t)}} + {^{{- {j\omega}_{0}}t}{a_{1}^{*}(t)}}} \right\rbrack + \left\lbrack {{^{{j2\omega}_{0}t}{a_{2}(t)}} + {^{{- {j2\omega}_{0}}t}{a_{2}^{*}(t)}}} \right\rbrack + \left\lbrack {{^{{j3\omega}_{0}t}{a_{3}(t)}} + {^{{- {j3\omega}_{0}}t}{a_{3}^{*}(t)}}} \right\rbrack + \ldots}}\mspace{79mu} {where}}\begin{matrix}{\mspace{79mu} {{a_{0}(t)} = {G_{0}\left( {{y_{1}(t)},{y_{2}(t)},{y_{3}(t)}} \right)}}} \\{= {{\frac{\alpha_{2}}{2^{2}}\left( {{2{y_{1}}^{2}} + {2{y_{2}}^{2}} + {2{y_{3}}^{2}}} \right)} + \ldots}}\end{matrix}\begin{matrix}{\mspace{79mu} {{a_{1}(t)} = {G_{1}\left( {{y_{1}(t)},{y_{2}(t)},{y_{3}(t)}} \right)}}} \\{= {{\frac{\alpha_{1}}{2}y_{1}} + {\frac{\alpha_{2}}{2^{2}}\left( {{2y_{1}^{*}y_{2}} + {2y_{2}^{*}y_{3}}} \right)} + \ldots}}\end{matrix}{{a_{2}(t)} = {{G_{2}\left( {{y_{1}(t)},{y_{2}(t)},{y_{3}(t)}} \right)} = {{\frac{\alpha_{1}}{2}y_{2}} + {\frac{\alpha_{2}}{2^{2}}\left( {y_{1}^{2} + {2y_{1}^{*}y_{3}}} \right)} + \ldots}}}\mspace{79mu} {{a_{3}(t)} = {{G_{3}\left( {{y_{1}(t)},{y_{2}(t)},{y_{3}(t)}} \right)} = {{\frac{\alpha_{1}}{2}y_{3}} + {\frac{\alpha_{2}}{2^{2}}2y_{1}y_{2}} + \ldots}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

A time index t is omitted for simple expression, and G_(i)(,,) denotes anonlinear function of the nonlinear power amplifier. All intermodulationterms are arranged in terms of K=3 in FIG. 4.

If relational expressions y₁(n)=F₁(x(n)), y₂(n)=F₂(x(n)), andy₂(n)=F₃(x(n)) are applied while the above Equation 4 is newlyrepresented in a discrete domain, the following Equation 5 can beobtained:

$\begin{matrix}{{a(n)} = {{a_{0}(n)} + \left\lbrack {{^{{j\omega}_{0}n}{a_{1}(n)}} + {^{{- {j\omega}_{0}}n}{a_{1}^{*}(n)}}} \right\rbrack + {\quad{\left\lbrack {{^{{j2\omega}_{0}n}{a_{2}(n)}} + {^{{- {j2\omega}_{0}}n}{a_{2}^{*}(n)}}} \right\rbrack + {\quad{\left\lbrack {{^{{j3\omega}_{0}n}{a_{3}(n)}} + {^{{- {j3\omega}_{0}}n}{a_{3}^{*}(n)}}} \right\rbrack + {\ldots \mspace{79mu} {where}\begin{matrix}{\mspace{79mu} {{a_{0}(n)} = {G_{0}\left( {{F_{1}(x)},{F_{2}(x)},{F_{3}\left( {x(n)} \right)}} \right.}}} \\{= {G_{0}\left( {{y_{1}(n)},{y_{2}(n)},{y_{3}(n)}} \right)}} \\{= {{\frac{\alpha_{2}}{2^{2}}\left( {{2{y_{1}}^{2}} + {2{y_{2}}^{2}} + {2{y_{3}}^{2}}} \right)} + \ldots}}\end{matrix}\begin{matrix}{\mspace{79mu} {{a_{1}(n)} = {G_{1}\left( {{F_{1}(x)},{F_{2}(x)},{F_{3}\left( {x(n)} \right)}} \right.}}} \\{= {G_{1}\left( {{y_{1}(n)},{y_{2}(n)},{y_{3}(n)}} \right)}} \\{= {{\frac{\alpha_{1}}{2}y_{1}} + {\frac{\alpha_{2}}{2^{2}}\left( {{2y_{1}^{*}y_{2}} + {2y_{2}^{*}y_{3}}} \right)} + \ldots}}\end{matrix}\begin{matrix}{\mspace{79mu} {{a_{2}(n)} = {G_{2}\left( {{F_{1}(x)},{F_{2}(x)},{F_{3}\left( {x(n)} \right)}} \right.}}} \\{= {G_{2}\left( {{y_{1}(n)},{y_{2}(n)},{y_{3}(n)}} \right)}} \\{= {{\frac{\alpha_{1}}{2}y_{2}} + {\frac{\alpha_{2}}{2^{2}}\left( {y_{1}^{2} + {2y_{1}^{*}y_{3}}} \right)} + \ldots}}\end{matrix}\begin{matrix}{\mspace{79mu} {{a_{3}(n)} = {G_{3}\left( {{F_{1}(x)},{F_{2}(x)},{F_{3}\left( {x(n)} \right)}} \right.}}} \\{= {G_{3}\left( {{y_{1}(n)},{y_{2}(n)},{y_{3}(n)}} \right)}} \\{= {{\frac{\alpha_{1}}{2}y_{3}} + {\frac{\alpha_{2}}{2^{2}}2y_{1}y_{2}} + \ldots}}\end{matrix}}}}}}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

A time index n is omitted for simple representation.

In an embodiment of the present invention, the problem of designingpredistorters from the output equation when N=3 is summarized byobtaining F₁( ) F₂( ) and F₃( ) that simultaneously satisfy thefollowing Equation 6:

a ₁(n)=G ₁(F ₁(x(n)),F ₂(x(n)),F ₃(x(x(n)))=x(n

a ₂(n)=G ₂(F ₁(x(n)),F ₂(x(n)),F ₃(x(n)))=0

a ₃(n)=G ₃(F ₁(x(n)),F ₂(x(n)),F ₃(x(n)))=0   Equation 6

However, in Equation 6, G_(i)(,,) is a nonlinear function, so that it isnot easy to directly and simultaneously solve individual items ofEquation 6.

Therefore, the configuration of a predistortion device according to apreferred embodiment of the present invention shown in FIG. 5 isproposed. However, in FIG. 5, the case of N=3 is exemplified, but it isapparent that N is a random number and is extensible.

As shown in FIG. 5, a digital predistortion device according to apreferred embodiment of the present invention includes a random signalgenerator (not shown); a nonlinear power amplifier (PA) 10; anequivalent amplifier model estimator 20; a coefficient extractor 30; andN predistorters 40.

The functions of the above components according to the present inventionwill be described below.

The nonlinear power amplifier 10 functions to receive N input signalsgenerated by the random signal generator, amplify the N input signals,and generate N output signals. The nonlinear power amplifier 10 of thepresent invention is a concept including even the model of a poweramplifier, as well as a power amplifier as an actual element.

The equivalent amplifier model estimator 20 functions to receive the Ninput signals and the N output signals of the nonlinear power amplifier10, and estimate the baseband characteristics of the nonlinear poweramplifier 10.

Further, when the N input signals and the N output signals for theequivalent amplifier model estimator 20 are not signals in the baseband,the procedure of respectively converting the input signals and theoutput signals into N input signals and N output signals in the basebandmay be added to the inside or the outside of the equivalent amplifiermodel estimator 20.

Furthermore, the coefficient extractor 30 extracts coefficients for thepre-distorters 40 using the estimated characteristics of the nonlinearpower amplifier 10.

The predistorters 40 may include harmonic elimination predistorters anda fundamental signal predistorter.

N-1 harmonic elimination predistorters function to eliminate second toNth harmonic signals from the N output signals of the nonlinear poweramplifier 10, and the fundamental signal predistorter functions tocompensate for the nonlinear characteristics of the fundamental signalamong the N output signals of the nonlinear power amplifier 10.

That is, the digital predistortion device according to an embodiment ofthe present invention can implement an adaptive coefficient algorithm byincluding the equivalent amplifier model estimator 20 and thecoefficient extractor 30, unlike the typical predistortion device ofFIG. 3.

The digital predistortion device of the present invention may furtherinclude Digital to Analog Converters (DACs) 50 for converting the Ninput signals for the nonlinear power amplifier 10 into analog signals;first mixers 60 for upconverting the N signals converted into the analogsignals; real operators 70 for selecting only real number signals fromamong the upconverted signals; second mixers 80 for downconverting theoutput signals of the nonlinear power amplifier 10; Analog to DigitalConverters (ADCs) 90 for converting the downconverted signals fromanalog signals into digital signals; and Low Pass Filters (LPFs) 100 foreliminating image signals generated during the procedure of performingconversion into the digital signals.

In the present invention according to the embodiment of FIG. 5, Equation6 can be changed to the following Equation 7:

a ₁(n)=G ₁(F ₁(x(n)),F ₂(F ₁(x(n))),F ₃(F ₂(F ₁(x(n)))))=x(n)

a ₂(n)=G ₂(y ₁(n),F ₂(y ₁(n)),F ₃(F ₂(y ₁(n))))=0

a ₃(n)=G ₃(y ₁(n),y ₂(n),F ₃(y ₂(n)))=0   Equation 7

In a new structure, for random input y₁(n) and y₂(n) in the lastexpression of Equation 7, F₃( ) can be obtained first. Thereafter, inthe second expression, F₃( ) is fixed, and then F₂( ) can be obtained.Finally, after F₂( ) and F₃( ) have been fixed, F₁( ) can be obtained inthe first expression. Therefore, harmonic signals can be eliminated bystages, and the N predistorters 40 for linearizing the fundamentalsignal can be designed. Further, even for higher harmonic signals,predistorters can be extended by stages in the same manner.

Below, a detailed embodiment of the present invention when N=3 will bedescribed in detail.

Estimation of Equivalent Power Amplifier Model

In a first stage, the equivalent amplifier model estimator 20 estimatesan equivalent amplifier model at the locations of harmonic frequenciesin the baseband of the nonlinear power amplifier 10. When the equivalentamplifier model of the fundamental signal is arranged based on Equation4 and FIG. 4, the following Equation 8 can be obtained:

$\begin{matrix}{\begin{matrix}{{a_{1}(n)} = {{w_{11}y_{1}} + {w_{12}y_{1}^{*}y_{2}} + {w_{13}y_{2}^{*}y_{3}} + {w_{14}y_{1}{y_{1}}^{2}} +}} \\{{{w_{15}y_{2}^{2}y_{3}^{*}} + {w_{16}y_{1}^{*2}y_{3}} + {w_{17}y_{1}{y_{2}}^{2}} + {w_{18}y_{1}{y_{3}}^{2}}}} \\{= {{w_{1}(n)}^{T}{u_{1}(n)}}}\end{matrix}\mspace{79mu} {where}\mspace{79mu} {{w_{1} = \left\lbrack {w_{11},w_{12},w_{13},w_{14},w_{15},w_{16},w_{17},w_{18}} \right\rbrack^{T}},\mspace{79mu} {{{and}{u_{1}(n)}} = {\begin{bmatrix}{{y_{1}(n)},{{y_{1}^{*}(n)}{y_{2}(n)}},{{y_{2}^{*}(n)}{y_{3}(n)}},{{y_{1}(n)}{{y_{1}(n)}}^{2}},} \\{{{y_{2}^{2}(n)}{y_{3}^{*}(n)}},{{y_{1}^{*2}(n)}{y_{3}(n)}},{{y_{1}(n)}{{y_{2}(n)}}^{2}},{{y_{1}(n)}{{y_{3}(n)}}^{2}}}\end{bmatrix}^{T}.}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

Each element of u₁(n) is a combination of y₁(n), y₂(n), and y₃(n) thatmake the output of the term e^(jω) ⁰ ^(n) in the output of the nonlinearpower amplifier 10. In this case, the number of the above coefficientsvaries according to the nonlinear order K of the nonlinear poweramplifier 10. For example, when K=3, the output has nonlinear termsranging to a third order. Similarly, the equivalent nonlinear poweramplifier models of second and third harmonic signals can be representedby the following Equations 9 and 10, respectively:

$\begin{matrix}{\begin{matrix}{\mspace{79mu} {{a_{2}(n)} = {{w_{21}y_{2}} + {w_{22}y_{1}^{2}} + {w_{23}y_{1}^{*}y_{3}} + {w_{24}y_{2}{y_{2}}^{2}} +}}} \\{{{w_{25}y_{2}{y_{1}}^{2}} + {w_{26}y_{2}{y_{3}}^{2}} + {w_{27}y_{1}y_{2}^{*}y_{3}}}} \\{= {{w_{2}(n)}^{T}{u_{2}(n)}}}\end{matrix}\mspace{79mu} {where}\mspace{79mu} {{w_{2} = \left\lbrack {w_{21},w_{22},w_{23},w_{24},w_{25},w_{26},w_{27}} \right\rbrack^{T}},\mspace{79mu} {and}}{{u_{2}(n)} = {\begin{bmatrix}{{y_{2}(n)},{y_{1}(n)}^{2},{{y_{1}(n)}^{*}{y_{3}(n)}},{{y_{2}(n)}{{y_{1}(n)}}^{2}},} \\{{{y_{2}(n)}{{y_{2}(n)}}^{2}},{{y_{2}(n)}{{y_{3}(n)}}^{2}},{{y_{1}(n)}{y_{2}^{*}(n)}{y_{3}(n)}}}\end{bmatrix}^{T}.}}} & {{Equation}\mspace{14mu} 9} \\{\begin{matrix}{\mspace{79mu} {{a_{3}(n)} = {{w_{31}y_{3}} + {w_{32}y_{1}y_{2}} + {w_{33}y_{1}^{3}} + {w_{34}y_{1}^{*}y_{2}^{2}} +}}} \\{{{w_{35}y_{3}{y_{3}}^{2}} + {w_{36}y_{3}{y_{1}}^{2}} + {w_{37}y_{3}{y_{2}}^{2}}}} \\{= {{w_{3}(n)}^{T}{u_{3}(n)}}}\end{matrix}\mspace{79mu} {where}\mspace{79mu} {{w_{3} = \left\lbrack {w_{31},w_{32},w_{33},w_{34},w_{35},w_{36},w_{37}} \right\rbrack^{T}},\mspace{79mu} {and}}\mspace{79mu} {{u_{3}(n)} = {\begin{bmatrix}{{y_{3}(n)},{{y_{1}(n)}{y_{2}(n)}},{y_{1}(n)}^{3},{{y_{1}^{*}(n)}{y_{2}(n)}^{2}},} \\{{{y_{3}(n)}{{y_{1}(n)}}^{2}},{{y_{3}(n)}{{y_{2}(n)}}^{2}},{{y_{3}(n)}{{y_{3}(n)}}^{2}}}\end{bmatrix}^{T}.}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

In the above Equations 8, 9, and 10, the examples of the nonlinear poweramplifier model were limited to third-degree polynomials. However, toimprove performance, the degree of a polynomial can be extended by asystem designer.

In Equations 9 and 10, individual elements of u₂(n) and u₃(n) arecombinations of y₁(n), y₂(n), and y₃(n) that make the output of termse^(j2ω) ⁰ ^(n) and e^(j3ω) ⁰ ^(n) in the output of the nonlinear poweramplifier 10. Cost functions required to obtain w₁, w₂, and w₃indicating the characteristics of the nonlinear power amplifier 10 aredefined by Equation 11:

ε_(w) ₁ =E{|e _(w) ₁ (n)|²},ε_(w) ₂ =E{|e _(w) ₂ (n)|²},ε_(w) ₃ =E{|e_(w) ₃ (n|²}  Equation 11

where e _(w) ₁ (n)=a ₁(n)−{circumflex over (w)}₁ ^(T)(n)u ₁(i)

e_(w) ₂ (n)=a₂(n)−ŵ₂ ^(T)(n)u₂(n), e_(w) ₃ (n)=a₃(n)−ŵ₃ ^(T)(n)u₃(n),and ŵ₁(n), ŵ₂(n), and ŵ₃(n) denote the estimation vectors of w₁, w₂, andw₃. In order to derive a Least Mean Squares (LMS) algorithm, Equation 11can be changed to the form of Equation 12.

ε_(w) ₁ =|e _(w) ₁ (n)|²,ε_(w) ₂ =|e _(w) ₂ (n)|²,ε_(w) ₃ =|e _(w) ₁(n)|²   Equation 12

Updated equations of ŵ₁(n), ŵ₂(n), and ŵ₃(n) for minimizing Equation 12are derived by the following Equation 13:

$\begin{matrix}{\begin{matrix}{{{\hat{w}}_{1}\left( {n + 1} \right)} = {{{\hat{w}}_{1}(n)} - {\frac{1}{2}\mu_{1}\frac{\partial{ɛ_{w_{1}}(n)}}{\partial{w_{1}(n)}}}}} \\{{= {{{\hat{w}}_{1}(n)} + {\mu_{1}{e_{w_{1}}^{*}(n)}u_{1}(n)}}},}\end{matrix}\begin{matrix}{{{\hat{w}}_{2}\left( {n + 1} \right)} = {{{\hat{w}}_{2}(n)} - {\frac{1}{2}\mu_{2}\frac{\partial{ɛ_{w_{2}}(n)}}{\partial{w_{2}(n)}}}}} \\{{= {{{\hat{w}}_{2}(n)} + {\mu_{2}{e_{w_{2}}^{*}(n)}u_{2}(n)}}},}\end{matrix}\begin{matrix}{{{\hat{w}}_{3}\left( {n + 1} \right)} = {{{\hat{w}}_{3}(n)} - {\frac{1}{2}\mu_{3}\frac{\partial{ɛ_{w_{3}}(n)}}{\partial{w_{3}(n)}}}}} \\{= {{{\hat{w}}_{3}(n)} + {\mu_{3}{e_{w_{3}}^{*}(n)}{u_{3}(n)}}}}\end{matrix}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

where each of μ₁, μ₂, and μ₃ denotes a step size required to controlconvergence speed and stability.

Extraction of Coefficients of Harmonic Elimination Predistorters

After the equivalent amplifier models have been estimated, coefficientsof the predistorters 40 for eliminating harmonics and linearizing afundamental signal can be extracted. First, after a third harmonicsignal has been eliminated based on an amplifier model for the thirdharmonic signal, a second harmonic signal is eliminated. The thirdpredistorter for eliminating the third harmonic signal can berepresented by the following Equation 14:

y ₃(n)=p ₃ ^(T) v ₃(n)   Equation 14

where p₃=[p₃₁,p₃₂,p₃₃,p₃₄,p₃₅,p₃₆,p₃₇, . . . ]^(T)

v ₃(n)=[y ₁(n)y ₂(n),y ₁(n)³ ,y ₁ ^(N)(n)y ₂ ,y ₁(n)³ |y ₁(n)|² ,y ₁(n)³|y ₂(n)|² ,y ₁ ^(t) (n)y ₂(n)² |y ₁(n)|² ,y ₁ ^(t) (n)y ₂(n)² |y ₂(n)|²,. . . |²

and the degree of the polynomial of the predistorter can be determinedby a designer.

Each element of v₃(n) is implemented as a combination of y₁(n) and y₂(n)that make e^(j3ω) ⁰ ^(n) in the output of the nonlinear power amplifier10. A cost function required to obtain the optimal coefficient of thethird predistorter is defined by the following Equation 15:

ε_(p) ₃ =|e _(p) ₃ (n)|²   Equation 15

where e_(p) ₃ (n)=0−ŵ₃ ^(T)u₃(n). That is, this is intended to minimizean output signal at the location of 3f_(c). An adaptive coefficientalgorithm for minimizing ε_(p) ₃ is derived by the following Equation16:

$\begin{matrix}\begin{matrix}{{{\hat{p}}_{3}\left( {n + 1} \right)} = {{{\hat{p}}_{3}(n)} - {\frac{1}{2}\mu_{p_{3}}\frac{\partial{ɛ_{p_{3}}(n)}}{\partial{p_{3}(n)}}}}} \\{= {{{\hat{p}}_{3}(n)} - {\frac{1}{2}\mu_{p_{3}}\frac{\partial{y_{3}(n)}}{\partial{p_{3}(n)}}\frac{\partial{{e_{p_{3}}(n)}}^{2}}{\partial{y_{3}(n)}}}}}\end{matrix} & {{Equation}\mspace{14mu} 16}\end{matrix}$

where μ_(p) ₃ denotes a step size.

Using the same manner, the coefficient update algorithm of a secondpredistorter for eliminating a second harmonic signal can be obtained.The second predistorter can be represented by the following Equation 17:

y ₂(n)=p ₂ ^(T) v ₂(n)   Equation 17

where p₂ =[p ₂₁,p₂₂,p₂₃,p₂₄, . . . ]^(T) and

v ₂(n)=[y ₁(n)² ,y ₁(n)² |y ₁(n)|²,y₁(n)² |y ₁(n)|⁴,y₁(n)² |y ₁(n)⁶, . .. |^(T).

Each element of v₂(n) is implemented as a combination of y₁(n) thatmakes e^(j2ω) ₀ ^(n) in the output of the amplifier, and the degree of apolynomial can be determined by the designer. A cost function requiredto obtain the optimal coefficient of the second predistorter is definedby the following Equation 18:

ε_(p) ₂ =|e _(p) ₂ (n)|²   Equation 18

where e_(p) ₂ (n)=0−ŵ₂ ^(T)u₂(n). That is, this is intended to minimizethe output signal at the location of 2f_(c). An adaptive coefficientalgorithm for minimizing ε_(p) ₂ is derived by the following Equation19:

$\begin{matrix}\begin{matrix}{{{\hat{p}}_{2}\left( {n + 1} \right)} = {{{\hat{p}}_{2}(n)} - {\frac{1}{2}\mu_{p_{2}}\frac{\partial{ɛ_{p_{2}}(n)}}{\partial{p_{2}(n)}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}\mu_{p_{2}}\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}{\mu_{p_{2}}\begin{bmatrix}{{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{3}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}{\mu_{p_{2}}\begin{bmatrix}{{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{y_{3}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}}\end{matrix} & {{Equation}\mspace{14mu} 19}\end{matrix}$

where μ_(p) ₂ denotes a step size.

After the third predistorter and the second predistorter for eliminatingharmonics have been designed through the above process, the coefficientof the first predistorter for linearizing the fundamental signal can beextracted.

Extraction of Coefficient of Predistorter for Linearizing FundamentalSignal

After the coefficients of the third predistorter and the secondpredistorter that were extracted above have been fixed, the coefficientof a fundamental signal predistorter that is a first predistorter isfinally extracted. The fundamental signal is implemented as an odd-ordercomponent, so that the first predistorter is represented by thefollowing Equation 20:

y ₁(n)=p ₁ ^(T) v ₁(n)   Equation 20

where p₁=[p₁₁,p₁₂,p₁₃,p₁₄, . . . ]^(T),

v₂(n)=[x(n),x(n)|x(n)x(n)]²,x(n)|x(n)|⁴,x(n)|x(n)|⁶, . . . ]^(T), andthe degree of the polynomial of the predistorter can be determined bythe designer.

A cost function required to obtain the coefficient of the firstpredistorter is defined by the following Equation 21:

ε_(p) ₁ |e _(p) ₁ (n)|²   Equation 21

where e_(p) ₁ (n)=x(n)−ŵ₁ ^(T)u₁(n). An adaptive coefficient algorithmfor minimizing Ε_(p) ₁ is derived by the following Equation 22:

$\begin{matrix}\begin{matrix}{{{\hat{p}}_{1}\left( {n + 1} \right)} = {{{\hat{p}}_{1}(n)} - {\frac{1}{2}\mu_{p_{1}}\frac{\partial{ɛ_{p_{1}}(n)}}{\partial{p_{1}(n)}}}}} \\{= {{{\hat{p}}_{1}(n)} - {\frac{1}{2}{\mu_{p_{1}}\begin{bmatrix}{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{1}(n)}}} +} \\{{\frac{\partial{y_{2}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{3}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}} \\{= {{{\hat{p}}_{1}(n)} - {\frac{1}{2}{\mu_{p_{1}}\begin{bmatrix}{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{1}(n)}}} +} \\{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{y_{2}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{y_{2}(n)}}{\partial{y_{1}(n)}}\frac{\partial{y_{3}(n)}}{\partial{y_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}}\end{matrix} & {{Equation}\mspace{14mu} 22}\end{matrix}$

where μ_(p) ₁ denotes a step size. After the harmonic eliminationpredistorters have been designed through the above process, thecoefficient of the fundamental signal predistorter that is the firstpredistorter for linearizing the fundamental signal can be estimated.

The digital predistortion method according to the embodiment of thepresent invention can be summarized as shown in FIG. 6.

That is, the digital predistortion method according to the presentinvention includes the step S200 of the random signal generatorgenerating N input signals; the step S300 of the nonlinear poweramplifier 10 amplifying the generated N input signals and thengenerating N output signals; the step S400 of the equivalent amplifiermodel estimator 20 receiving the N input signals and the N outputsignals, and estimating the characteristics of the nonlinear poweramplifier 10; the step S500 of the coefficient extractor 30 extractingcoefficients for harmonic elimination predistorters and a fundamentalsignal predistorter using the estimated characteristics of the nonlinearpower amplifier; the step S600 of N-1 harmonic elimination predistorterseliminating second or higher harmonic signals from the N output signals;and the step S700 of the fundamental signal predistorter compensatingfor nonlinear characteristics occurring in the fundamental signal amongthe N output signals.

Further, FIG. 7 illustrates the procedure for preprocessing inputsignals to be input to the nonlinear power amplifier 10.

As shown in FIG. 7, the digital predistortion method according to thepresent invention may further include, between step S200 and step S300,the step S210 of the DACs 50 converting the N input signals into analogsignals; the step S220 of the first mixers 60 upconverting the signalsconverted into the analog signals; the step S230 of the real operators70 selecting real number signals from among the upconverted signals; andthe step S240 of inputting the real number signals selected at step S230to the nonlinear power amplifier 10.

FIG. 8 is a flowchart showing the processing of signals to be input tothe equivalent amplifier model estimator 20.

That is, the digital predistortion method according to the presentinvention includes the step S310 of inputting the N output signals ofthe nonlinear power amplifier 10 to the second mixers 80 anddownconverting the N output signals; the step S320 of the ADCs 90converting the downconverted signals into digital signals; and the stepS330 of the low pass filters 100 eliminating image signals fromimaginary numbers of the signals converted into the digital signals, inorder to process the signals to be input to the equivalent amplifiermodel estimator 20.

A detailed flowchart showing the detailed coefficient extraction stepS500 performed by the coefficient extractor 30 is illustrated in FIG. 9.As shown in FIG. 9, the coefficient extraction step may include the stepS510 of first extracting the coefficient of a harmonic eliminationpredistorter corresponding to a harmonic of the highest frequency amongthe N-1 harmonic elimination predistorters, and extracting thecoefficients of harmonic elimination predistorters corresponding toharmonics of lower frequencies by stages; and the step S520 ofextracting and fixing all the coefficients of the harmonic eliminationpredistorters and thereafter extracting the coefficient of thefundamental signal predistorter.

Verification of Effects

In order to verify the effects of the present invention, computersimulation was conducted. The environment of the simulation is shown inFIG. 10. As a transmission signal x(n) for a transmitter, a signalobtained by filtering a 16-Quadrature Amplitude Modulated (QAM) signalusing a Square Root Raised Cosine (SRRC) filter having a roll-off valueof 0.25 and a 10-times oversampled value was used. In order to verifythe output of the amplifier in a passband, a 10-times oversampled signalis processed via predistorter blocks, the processed signal is 20-timesupsampled, the upsampled signal is upconverted by a mixer, and theupconverted signal is input to a passband power amplifier. In a feedbackpath, in order to estimate an equivalent amplifier model and thecoefficients of predistorters, frequency signals f_(c), 2f_(c), and3f_(c) are downconverted and filtered, and resulting signals are20-times downsampled. The nonlinear power amplifier used in thesimulation can be represented by the following Equation 23:

a(n)=y(n)−0.8y(n)²+0.7y(n)³   Equation 23

FIG. 11 illustrates harmonic elimination performance when thepredistortion scheme proposed in the present invention was applied.

As can be seen from FIG. 11, when predistorters are not applied, afundamental signal is output at the location of a frequency f_(c), andharmonic signals are generated at the locations of 2f_(c) and 3f_(c) tocause undesirable interference signals. In order to eliminate suchharmonic signals, when the predistortion scheme proposed in the presentinvention is applied, it can be seen that the harmonic signals can bereduced by about 40 dB at the location of 2f_(c) and by about 20 dB atthe location of 3f_(c).

FIGS. 12, 13, and 14 illustrate frequency spectra obtained by convertingsignals at respective frequency locations into baseband signals, andviewed at the respective frequency locations. It can be seen that bymeans of linearization based on the predistortion scheme proposed inFIG. 8, interference could be reduced in a band adjacent to thefundamental signal by about 20 dB or more. In FIGS. 13 and 14, theattenuation of harmonic signals caused by nonlinearity can be verified.It can be seen that in FIG. 13, a second harmonic signal was reduced byabout 40 dB, and in FIG. 14, a third harmonic signal was reduced byabout 20 dB.

From the above description, it can be seen that second or higherharmonic signals can be effectively eliminated while a fundamentalsignal can also be linearized, by using the new predistortion schemeproposed in the present invention. The present invention is determinedto be usefully applied to a CR system, and can be used to eliminateharmonics even in conventional systems.

Mode for Invention

1. A digital predistortion device for a broadband power amplifier,comprising: a nonlinear power amplifier for amplifying N input signalsgenerated by a random signal generator, and then generating N outputsignals; an equivalent amplifier model estimator for receiving the Ninput signals and the N output signals, and estimating characteristicsof the nonlinear power amplifier; a coefficient extractor for extractingcoefficients of N predistorters using the estimated characteristics ofthe nonlinear power amplifier; and N predistorters for eliminating orcompensating for all or part of the N output signals.
 2. The digitalpredistortion device of claim 1, wherein the N predistorters comprise:N-1 harmonic elimination predistorters for eliminating second to Nthharmonic signals from the N output signals of the nonlinear poweramplifier; and a fundamental signal predistorter for compensating fornonlinear characteristics of a fundamental signal among the N outputsignals of the nonlinear power amplifier.
 3. The digital predistortiondevice of claim 1, further comprising: Digital to Analog Converters(ADCs) for converting the N input signals into analog signals; firstmixers for upconverting the N signals converted into analog signals;real operators for selecting real number signals from among theupconverted signals; second mixers for downconverting the N outputsignals of the nonlinear power amplifier; Analog to Digital Converters(ADCs) for converting the downconverted signals into digital signals;and low pass filters for eliminating image signals from the signalsconverted into the digital signals.
 4. The digital predistortion deviceof claim 1, wherein the estimation of the characteristics of thenonlinear power amplifier performed by the equivalent amplifier modelestimator for the fundamental signal can be represented by the followingEquation: $\begin{matrix}{{a_{1}(n)} = {{w_{11}y_{1}} + {w_{12}y_{1}^{*}y_{2}} + {w_{13}y_{2}^{*}y_{3}} + {w_{14}y_{1}{y_{1}}^{2}} +}} \\{{{w_{15}y_{2}^{2}y_{3}^{*}} + {w_{16}y_{1}^{*2}y_{3}} + {w_{17}y_{1}{y_{2}}^{2}} + {w_{18}y_{1}{y_{3}}^{2}}}} \\{= {{w_{1}(n)}^{T}{u_{1}(n)}}}\end{matrix}$      where     w₁ = [w₁₁, w₁₂, w₁₃, w₁₄, w₁₅, w₁₆, w₁₇, w₁₈]^(T),      and${u_{1}(n)} = \begin{bmatrix}{{y_{1}(n)},{{y_{1}^{*}(n)}{y_{2}(n)}},{{y_{2}^{*}(n)}{y_{3}(n)}},{{y_{1}(n)}{{y_{1}(n)}}^{2}},} \\{{{y_{2}^{2}(n)}{y_{3}^{*}(n)}},{{y_{1}^{*2}(n)}{y_{3}(n)}},{{y_{1}(n)}{{y_{2}(n)}}^{2}},{{y_{1}(n)}{{y_{3}(n)}}^{2}}}\end{bmatrix}^{T}$ (where w₁ denotes a coefficient indicating thecharacteristics of the nonlinear power amplifier, y₁(n), y₂(n), . . .denote the N input signals of the nonlinear power amplifier, y*₁(n),y*₂(n), . . . denote complex conjugates of the N input signals, whereinan example of a nonlinear power amplifier model is limited tothird-degree polynomials, but a degree of a polynomial can be extendedby a system designer to improve performance).
 5. The digitalpredistortion device of claim 1, wherein the estimation of thecharacteristics of the nonlinear power amplifier performed by theequivalent amplifier model estimator for second and third harmonicsignals can be represented by the following Equations (5-1) and (5-2):$\begin{matrix}{\begin{matrix}{{a_{2}(n)} = {{w_{21}y_{2}} + {w_{22}y_{1}^{2}} + {w_{23}y_{1}^{*}y_{3}} + {w_{24}y_{2}{y_{2}}^{2}} +}} \\{{{w_{25}y_{2}{y_{1}}^{2}} + {w_{26}y_{2}{y_{3}}^{2}} + {w_{27}y_{1}y_{2}^{*}y_{3}}}} \\{= {{w_{2}(n)}^{T}{u_{2}(n)}}}\end{matrix}{where}{{w_{2} = \left\lbrack {w_{21},w_{22},w_{23},w_{24},w_{25},w_{26},w_{27}} \right\rbrack^{T}},{and}}{{{u_{2}(n)} = \begin{bmatrix}{{y_{2}(n)},{y_{1}(n)}^{2},{{y_{1}(n)}^{*}{y_{3}(n)}},{{y_{2}(n)}{{y_{1}(n)}}^{2}},} \\{{{y_{2}(n)}{{y_{2}(n)}}^{2}},{{y_{2}(n)}{{y_{3}(n)}}^{2}},{{y_{1}(n)}{y_{2}^{*}(n)}{y_{3}(n)}}}\end{bmatrix}^{T}},}} & \left( {5\text{-}1} \right) \\{\begin{matrix}{{a_{3}(n)} = {{w_{31}y_{3}} + {w_{32}y_{1}y_{2}} + {w_{33}y_{1}^{3}} + {w_{34}y_{1}^{*}y_{2}^{2}} +}} \\{{{w_{35}y_{3}{y_{3}}^{2}} + {w_{36}y_{3}{y_{1}}^{2}} + {w_{37}y_{3}{y_{2}}^{2}}}} \\{= {{w_{3}(n)}^{T}{u_{3}(n)}}}\end{matrix}{where}{{w_{3} = \left\lbrack {w_{31},w_{32},w_{33},w_{34},w_{35},w_{36},w_{37}} \right\rbrack^{T}},{and}}{{u_{3}(n)} = \begin{bmatrix}{{y_{3}(n)},{{y_{1}(n)}{y_{2}(n)}},{y_{1}(n)}^{3},{{y_{1}^{*}(n)}{y_{2}(n)}^{2}},} \\{{{y_{3}(n)}{{y_{1}(n)}}^{2}},{{y_{3}(n)}{{y_{2}(n)}}^{2}},{{y_{3}(n)}{{y_{3}(n)}}^{2}}}\end{bmatrix}^{T}}} & \left( {5\text{-}2} \right)\end{matrix}$ (where w₂ and w₃ denote coefficients indicating thecharacteristics of the nonlinear power amplifier, y₁(n), y₂(n), . . .denote the N input signals of the nonlinear power amplifier, and y*₁(n),y*₂(n), . . . denote complex conjugates of the N input signals, whereinan example of a nonlinear power amplifier model is limited tothird-degree polynomials, but a degree of a polynomial can be extendedby a system designer to improve performance).
 6. The digitalpredistortion device of claim 4, wherein cost functions for w₁, w₂, andw₃ indicating the characteristics of the nonlinear power amplifier arerepresented by the following Equation:ε_(w) ₁ =E{|e _(w) ₁ (n)|²}, ε_(w) ₂ =E{|e _(w) ₂ (n)|²}, ε_(w) ₃ =E{|e_(w) ₂(n)|²} (where e_(w) ₁ (n)=a₁(n)−ŵ₁ ^(T)(n)u₁(i), e_(w) ₂(n)=a₂(n)−ŵ₂ ^(T)(n)u₂(n), e_(w) ₁ (n)=a₃(n)−ŵ₃ ^(T)(n)u₃(n), and ŵ₁(n),ŵ₂(n), and ŵ₃(n) denote estimation vectors of w₁, w₂, and w₃,respectively).
 7. The digital predistortion device of claim 4, whereincost functions for w₁, w₂, and w₃ indicating the characteristics of thenonlinear power amplifier are represented by the following Equation toderive a Least Mean Squares (LMS) algorithm:ε_(w) ₁ =|e _(w) ₁ (n)|²,ε_(w) ₂ =|e _(w) ₂ (n)|²,ε_(w) ₃ =|e _(w) ₃(n)|² (where e_(w) ₁ (n)=a₁(n)−ŵ₁ ^(T)(n)u₁(i), e_(w) ₂ (n)=a₂(n)−ŵ₂^(T)(n)u₂(n), e_(w) ₃ (n)=a₃(n)−ŵ₃ ^(T)(n)u₃(n), and ŵ₁(n), ŵ₂(n), andŵ₃(n) denote estimation vectors of w₁, w₂, and w₃, respectively).
 8. Thedigital predistortion device of claim 7, wherein updated equations ofŵ₁(n), ŵ₂(n), and ŵ₃(n) for minimizing the cost functions arerepresented by the following Equations: $\begin{matrix}{{{\hat{w}}_{1}\left( {n + 1} \right)} = {{{\hat{w}}_{1}(n)} - {\frac{1}{2}\mu_{1}\frac{\partial{ɛ_{w_{1}}(n)}}{\partial{w_{1}(n)}}}}} \\{{= {{{\hat{w}}_{1}(n)} + {\mu_{1}{e_{w_{1}}^{*}(n)}u_{1}(n)}}},}\end{matrix}$ $\begin{matrix}{{{\hat{w}}_{2}\left( {n + 1} \right)} = {{{\hat{w}}_{2}(n)} - {\frac{1}{2}\mu_{2}\frac{\partial{ɛ_{w_{2}}(n)}}{\partial{w_{2}(n)}}}}} \\{{= {{{\hat{w}}_{2}(n)} + {\mu_{2}{e_{w_{2}}^{*}(n)}u_{2}(n)}}},}\end{matrix}$ $\begin{matrix}{{{\hat{w}}_{3}\left( {n + 1} \right)} = {{{\hat{w}}_{3}(n)} - {\frac{1}{2}\mu_{3}\frac{\partial{ɛ_{w_{3}}(n)}}{\partial{w_{3}(n)}}}}} \\{= {{{\hat{w}}_{3}(n)} + {\mu_{3}{e_{w_{3}}^{*}(n)}{u_{3}(n)}}}}\end{matrix}$ (where each of μ₁, μ₂, and μ₃ denotes a step size requiredto control convergence speed and stability).
 9. The digitalpredistortion device of claim 2, wherein the coefficient extractor isconfigured to first extract a coefficient of a harmonic eliminationpredistorter corresponding to a harmonic of a highest frequency amongthe N-1 harmonic elimination predistorters, and then extractcoefficients of harmonic elimination predistorters corresponding toharmonics of lower frequencies by stages.
 10. The digital predistortiondevice of claim 2, wherein the coefficient extractor is configured toextract and fix all coefficients of the harmonic eliminationpredistorters, and thereafter extract a coefficient of the fundamentalsignal predistorter.
 11. The digital predistortion device of claim 9,wherein a harmonic elimination predistorter for eliminating a thirdharmonic signal, a cost function for obtaining a coefficient of theharmonic elimination predistorter, and an adaptive coefficient algorithmfor minimizing the cost function are respectively represented by thefollowing Equations (11-1), (11-2), and (11-3) when N=3,y ₃(n)=p ₃ ^(T) v ₃(n)   (11-1)where p₃=[p₃₁,p₃₂,p₃₃,p₃₄,p₃₅,p₃₆,p₃₇, . . .]^(T),v ₃(n)=[y ₃(n)y ₂(n)y ₁(n)² y* ₁(n)y ₂(n)² ,y ₂(n)³ |y ₁(n)|² ,y ₁(n)³|y ₂(n)|² ,y* ₁(n)y ₂(n)² y ₁(n)|² ,y* ₁(n)y ₂(n)² |y ₂(n)|², . . .]^(T), and y₁(n) and y₂(n) denote first and second input signals of thenonlinear power amplifier, wherein a degree of a polynomial of thepredistorter can be determined by a designer),ε_(p) ₃ =|e _(p) ₃ (n)|²   (11-2) (where e_(p) ₁ (n)=0−ŵ₃ ^(T)(n)u₃(n)),and $\begin{matrix}\begin{matrix}{{{\hat{p}}_{3}\left( {n + 1} \right)} = {{{\hat{p}}_{3}(n)} - {\frac{1}{2}\mu_{p_{3}}\frac{\partial{ɛ_{p_{3}}(n)}}{\partial{p_{3}(n)}}}}} \\{= {{{\hat{p}}_{3}(n)} - {\frac{1}{2}\mu_{p_{3}}\frac{\partial{y_{3}(n)}}{\partial{p_{3}(n)}}\frac{\partial{{e_{p_{3}}(n)}}^{2}}{\partial{y_{3}(n)}}}}}\end{matrix} & \left( {11\text{-}3} \right)\end{matrix}$ (where μ_(p) ₃ denotes a step size).
 12. The digitalpredistortion device of claim 9, wherein a harmonic eliminationpredistorter for eliminating a second harmonic signal, a cost functionfor obtaining a coefficient of the harmonic elimination predistorter,and an adaptive coefficient algorithm for minimizing the cost functionare respectively represented by the following Equations (12-1), (12-2),and (12-3) when N=3,y ₂(n)=p ₂ ^(T) v ₂(n)   (12-1)(where p₂=[p₂₁,p₂₂,p₂₃,p₂₄, . . . ]^(T),v₂(n)=[y₁(n)²,y₁(n)²|y₁(n)|²,y₁(n)²|y₁(n)|⁴,y₁(n)²|y₁(n)|⁶, . . . ]^(T),and y₁(n) denotes a first input signal of the nonlinear power amplifier,wherein a degree of a polynomial of the predistorter can be determinedby a designer), $\begin{matrix}{{ɛ_{p_{2}} = {{e_{p_{2}}(n)}}^{2}}{\left( {{{where}\mspace{14mu} {e_{p_{2}}(n)}} = {0 - {{\hat{w}}_{2}^{T}{u_{2}(n)}}}} \right),{and}}} & \left( {12\text{-}2} \right) \\\begin{matrix}{{{\hat{p}}_{2}\left( {n + 1} \right)} = {{{\hat{p}}_{2}(n)} - {\frac{1}{2}\mu_{p_{2}}\frac{\partial{ɛ_{p_{2}}(n)}}{\partial{p_{2}(n)}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}\mu_{p_{2}}\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}{\mu_{p_{2}}\begin{bmatrix}{{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{3}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}} \\{= {{{\hat{p}}_{2}(n)} - {\frac{1}{2}{\mu_{p_{2}}\begin{bmatrix}{{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{2}(n)}}{\partial{p_{2}(n)}}\frac{\partial{y_{3}(n)}}{\partial{y_{2}(n)}}\frac{\partial{{e_{p_{2}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}}\end{matrix} & \left( {12\text{-}3} \right)\end{matrix}$ (where μ_(p) ₂ denotes a step size).
 13. The digitalpredistortion device of claim 10, wherein the fundamental signalpredistorter for compensating for nonlinear characteristics occurring inthe fundamental signal, a cost function for obtaining a coefficient ofthe fundamental signal predistorter, and an adaptive coefficientalgorithm for minimizing the cost function are respectively representedby the following Equations (13-1), (13-2), and (13-3) when N=3:y ₁(n)=p ₁ ^(T) v ₁(n)   (13-1)(where p₁=[p₁₁,p₁₂,p₁₃,p₁₄, . . . ]^(T),v₂(n)=[x(n),x(n)|x(n)|²,x(n)|x(n)|⁴,x(n)|x(n)|⁶, . . . ]^(T), and x(n)denotes a transmission signal for a transmitter to be input to thefundamental signal predistorter, wherein a degree of a polynomial of thepredistorter can be determined by the designer), $\begin{matrix}{{ɛ_{p_{1}} = {{e_{p_{1}}(n)}}^{2}}{\left( {{{where}\mspace{14mu} {e_{p_{1}}(n)}} = {{x(n)} - {{\hat{w}}_{1}^{T}{u_{1}(n)}}}} \right),{and}}} & \left( {13\text{-}2} \right) \\\begin{matrix}{{{\hat{p}}_{1}\left( {n + 1} \right)} = {{{\hat{p}}_{1}(n)} - {\frac{1}{2}\mu_{p_{1}}\frac{\partial{ɛ_{p_{1}}(n)}}{\partial{p_{1}(n)}}}}} \\{= {{{\hat{p}}_{1}(n)} - {\frac{1}{2}{\mu_{p_{1}}\begin{bmatrix}{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{1}(n)}}} +} \\{{\frac{\partial{y_{2}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{3}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}} \\{= {{{\hat{p}}_{1}(n)} -}} \\{{\frac{1}{2}{\mu_{p_{1}}\begin{bmatrix}{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{1}(n)}}} +} \\{{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{y_{2}(n)}}{\partial{y_{1}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{2}(n)}}} +} \\{\frac{\partial{y_{1}(n)}}{\partial{p_{1}(n)}}\frac{\partial{y_{2}(n)}}{\partial{y_{1}(n)}}\frac{\partial{y_{3}(n)}}{\partial{y_{2}(n)}}\frac{\partial{{e_{p_{1}}(n)}}^{2}}{\partial{y_{3}(n)}}}\end{bmatrix}}}}\end{matrix} & \left( {13\text{-}3} \right)\end{matrix}$ (where μ_(p) ₁ denotes a step size).
 14. A digitalpredistortion method for a broadband power amplifier, comprising: (a) arandom signal generator generating N input signals; (b) a nonlinearpower amplifier amplifying the generated N input signals, and thengenerating N output signals; (c) an equivalent amplifier model estimatorreceiving the N input signals and the N output signals, and estimatingcharacteristics of the nonlinear power amplifier; (d) a coefficientextractor extracting coefficients for N-1 harmonic eliminationpredistorters and a single fundamental signal predistorter using theestimated characteristics of the nonlinear power amplifier; (e) the N-1harmonic elimination predistorters eliminating second or higher harmonicsignals from the N output signals; and (f) the fundamental signalpredistorter compensating for nonlinear characteristics occurring in afundamental signal among the N output signals.
 15. The digitalpredistortion method of claim 14, further comprising, between (a) and(b): (a-1) Digital to Analog Converters (DACs) converting the N inputsignals into analog signals; (a-2) first mixers upconverting the signalsconverted into the analog signals; (a-3) real operators selecting realnumber signals from among the upconverted signals; and (a-4) inputtingthe real number signals selected at (a-3) to the nonlinear poweramplifier.
 16. The digital predistortion method of claim 14, furthercomprising, between (b) and (c): (b-1) inputting the N output signals ofthe nonlinear power amplifier to second mixers and downconverting the Noutput signals; (b-2) Analog to Digital Converters (ADCs) converting thedownconverted signals into digital signals; and (b-3) low pass filterseliminating imagine signals from the signals converted into the digitalsignals.
 17. The digital predistortion method of any one of claims claim14, wherein (d) comprises: first extracting a coefficient of a harmonicelimination predistorter corresponding to a harmonic of a highestfrequency among the N-1 harmonic elimination predistorters, and thenextracting coefficients of harmonic elimination predistorterscorresponding to harmonics of lower frequencies by stages; andextracting and fixing all coefficients of the N-1 harmonic eliminationpredistorters, and thereafter extracting a coefficient of thefundamental signal predistorter.
 18. The digital predistortion device ofclaim 2, further comprising: Digital to Analog Converters (ADCs) forconverting the N input signals into analog signals; first mixers forupconverting the N signals converted into analog signals; real operatorsfor selecting real number signals from among the upconverted signals;second mixers for downconverting the N output signals of the nonlinearpower amplifier; Analog to Digital Converters (ADCs) for converting thedownconverted signals into digital signals; and low pass filters foreliminating image signals from the signals converted into the digitalsignals.
 19. The digital predistortion device of claim 5, wherein costfunctions for w₁, w₂, and w₃ indicating the characteristics of thenonlinear power amplifier are represented by the following Equation:ε_(w) ₃ =E{|e _(w) ₁(n)|²},ε_(w) ₂ =E{|e _(w) ₂ (n)|²},ε_(w) ₃ =E{|e_(w) ₂ (n)|²} (where e_(w) ₁ (n)=a₁(n)−ŵ₁ ^(T)(n)u₁(i). e_(w) ₂(n)=a₂(n)−ŵ₂ ^(T)(n)u₂(n), e_(w) ₃ (n)=a₃(n)−ŵ₃ ^(T)(n)u₃(n), and ŵ₁(n),ŵ₂(n), and ŵ₃(n) denote estimation vectors of w₁, w₂ , and w₃ ,respectively).
 20. The digital predistortion device of claim 5, whereincost functions for w₁, w₂, and w₃ indicating the characteristics of thenonlinear power amplifier are represented by the following Equation toderive a Least Mean Squares (LMS) algorithm:ε_(w) ₁ =|e _(w) ₁ (n)|²,ε_(w) ₂ =|e _(w) ₂ (n)|²,ε_(w) ₃ =|e _(w) ₃(n)|² (where e_(w) ₁ (n)=a₁(n)−ŵ₁ ^(T)(n)u₁(i), e_(w) ₂ (n)=a₂(n)−ŵ₂^(T)(n)u₂(n), e_(w) ₃ (n)=a₃(n)−ŵ₃ ^(T)(n)u₃(n), and ŵ₁(n), ŵ₂(n), andŵ₃(n) denote estimation vectors of w₁, w₂, and w₃, respectively).